(A) The equation of a circle with centre $z_0$ and radius $r$ is given by $|z - z_0| = r$.Squaring both sides,we get $|z - z_0|^2 = r^2$.Using the pro

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$z\bar{z} - z\bar{z_0} - \bar{z}z_0 + z_0\bar{z_0} = r^2$

(A) The equation of a circle with centre $z_0$ and radius $r$ is given by $|z - z_0| = r$.Squaring both sides,we get $|z - z_0|^2 = r^2$.Using the property $|w|^2 = w\bar{w}$,we have $(z - z_0)(\overline{z - z_0}) = r^2$.$(z - z_0)(\bar{z} - \bar{z_0}) = r^2$.Expanding the product,we get $z\bar{z} - z\bar{z_0} - \bar{z}z_0 + z_0\bar{z_0} = r^2$.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

Medium

$A$ circle whose radius is $r$ and centre is $z_0$,then the equation of the circle is

A
$z\bar{z} - z\bar{z_0} - \bar{z}z_0 + z_0\bar{z_0} = r^2$
B
$z\bar{z} + z\bar{z_0} - \bar{z}z_0 + z_0\bar{z_0} = r^2$
C
$z\bar{z} - z\bar{z_0} + \bar{z}z_0 - z_0\bar{z_0} = r^2$
D
None of these

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4-1.Complex numbers

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$A$ circle whose radius is $r$ and centre is $z_0$,then the equation of the circle is

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